Recall how resistance depends on charge carriers

The electrical conductivity is $\sigma = n e \mu$ where:

• $n$ = number density of charge carriers
• $e$ = electronic charge
• $\mu$ = mobility

Hence resistance depends on both:

• the number of charge carriers
• their mobility/scattering

For metals

In a metal, the number of free electrons is approximately constant with temperature.

So, with increase in temperature, the main effect is increased lattice vibrations, which increase scattering and reduce mobility.

Therefore, resistance of a metal increases with temperature.

For semiconductors

In a semiconductor, when temperature increases, a large number of additional electron-hole pairs are thermally generated.

Thus, the carrier concentration $n$ increases sharply with temperature.

Although scattering also increases, the increase in carrier concentration is the dominant effect.

Therefore, resistance of a semiconductor decreases with temperature.

Essential difference

The key distinction between metals and semiconductors is that in semiconductors the number of charge carriers changes strongly with temperature, whereas in metals it remains nearly constant.

So the essential reason for the different variation of resistance with temperature is: $\boxed{\text{variation of the number of charge carriers with temperature}}$

Check options

• A: crystal structure — not the essential reason.
• B: variation of the number of charge carriers with temperature — correct.
• C: type of bonding — not the direct reason.
• D: variation of scattering mechanism with temperature — scattering changes in both, but this is not the essential difference causing opposite behavior.

Final answer

$\boxed{\text{B}}$